INFINITELY MANY SEGREGATED SOLUTIONS FOR COUPLED NONLINEAR SCHRODINGER SYSTEMS

In this paper, we consider the following coupled nonlinear Schrodinger system {-Delta u + (1 + delta a(x))u = mu(1)u(3) + beta uv(2) in R-3, -Delta v + (1 + delta b(x))v = mu(2)v(3)+ beta u(2)v in R-3, u -> 0, v -> 0, as vertical bar x vertical bar -> infinity where mu(1) > 0, mu(2) > 0, beta is an element of R, delta is an element of R, and a(x) and b(x) are two C-alpha potentials with 0 < alpha < 1, satisfying some slow decay assumptions, but do not need to fulfill any symmetry property. Using the Lyapunov-Schmidt reduction method and some variational techniques, we show that there exist 0 < delta(0) < 1 and 0 < beta(0) < min {mu(1), mu(2)} such that the above system has infinitely many positive segregated solutions for any 0 < delta < delta(0) and 0 < beta < beta(0).